Optimized Implementation for Calculation and Fast-Update of Pfaffians Installed to the Open-Source Fermionic Variational Solver mVMC

Abstract

In this article, we present a high performance, portable and well templated implementation for computing and fast-updating Pfaffian and inverse of an even-ranked skew-symmetric (antisymmetric) matrix. It is achieved with a skew-symmetric, blocked variant of the Parlett-Reid algorithm and a blocked update scheme based on the Woodbury matrix identity. Installation of this framework into the geminal-wavefunction-based many-variable Variational Monte Carlo (mVMC) code boosts sampling performance to up to more than $6$ times without changing Markov chain's behavior. The implementation is based on an extension of the BLAS-like instantiation software (BLIS) framework which has optimized kernel for many state-of-the-art processors including Intel Skylake-X, AMD EPYC Rome and Fujitsu A64FX.

arXiv comment18 pages, 3 figures and 3 tables. Source code presented in this work can be obtained from http://github.com/issp-center-dev/mVMC/tree/develop

References in corpus (20)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• The ARM Scalable Vector Extension
• Variational optimization with infinite projected entangled-pair states
• Superconductivity in the two-dimensional t-J model
• Gradient methods for variational optimization of projected entangled-pair states
• Efficient numerical computation of the Pfaffian for dense and banded skew-symmetric matrices
• Nature of the spin liquid state of the Hubbard model on honeycomb lattice
• Quantum Spin Liquid in Spin 1/2 J1-J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections
• mVMC - Open-source software for many-variable variational Monte Carlo method
• Quantum Lattice Model Solver $\mathcal{H}\Phi$
• Competition among various charge-inhomogeneous states and d-wave superconducting state in Hubbard models on square lattices
• Variational Monte Carlo study of chiral spin liquid in the extended Heisenberg model on the Kagome lattice
• Vertical Density Matrix Algorithm: A Higher-Dimensional Numerical Renormalization Scheme based on the Tensor Product State Ansatz
• Superconductivity and its mechanism in an ab initio model for electron-doped LaFeAsO
• Ab Initio Study on Superconductivity and Inhomogeneity in Hg-based Cuprate Superconductor
• Charge dynamics of correlated electrons: Variational description with inclusion of composite fermions